Understanding Statistical Power and Sample Size in Research

Research Fundamentals #5

Learning Approach
This lesson builds upon our understanding of Alpha (α) and Beta (β) Levels. If you haven’t reviewed those concepts yet, go back and do so first—each step in this series follows a structured learning approach.

The Importance of Sample Size in Research

Selecting an appropriate sample size is crucial in hypothesis testing. An inadequate sample size will lead to unreliable results, increased errors. Too large aa sample size can lead to wasted resources. Something Institutional Review Boards (IRB’s) focus heavily on. More on the IRB later.
=Dr. Santangelo
Tweet

Factors That Influence Sample Size

Effect Size: The magnitude of the difference or relationship being studied.
Significance Level (α): Lower α requires a larger sample to detect true effects.
Power (1 – β): Higher power requires a larger sample to reduce Type II errors.
Variability in Data: High variability means a larger sample is needed for reliable conclusions.
Study Design: Different experimental setups may demand different sample sizes.

Power is the probability of correctly rejecting the null hypothesis (H₀) when the alternative hypothesis (H₁) is true. Remember it is calculated it is calculated as
Power (1 – β):
-Dr. Santangelo
Tweet

Key Points

Power Analysis: Ensuring Sufficient Statistical Power

A higher power (typically 80% or 0.80) means there is a low probability (20%) of missing a real effect.
Increasing power reduces Type II errors but may require a larger sample size.
Researchers *should* conduct power analysis to determine the minimum sample size needed to achieve an adequate power level.

Conducting a Power Analysis
Steps to Determine Sample Size:

Define Alpha (α): The acceptable risk of a Type I error (commonly 0.05).
Set Beta (β) and Power: Typically, β = 0.20 (power = 0.80).
Estimate Effect Size: Use previous research or pilot studies to determine a meaningful difference.
Consider Variability: More variation in data requires a larger sample size.
Use Statistical Software Programs like G*Power, R, or SPSS calculate required sample sizes.

Example

Researchers want to determine the effectiveness of a new therapy treatment. The researchers define α = 0.05, power = 0.80, and estimate an effect size of 0.5 (moderate effect). A power analysis may suggest a sample size of 100 participants pe therapy group.

Balancing Practicality and Precision

Increasing▲ sample size improves accuracy. researchers must also consider:
•Time and Cost Constraints: Larger samples require more resources.
•Ethical Considerations: In medical research, using too many participants unnecessarily is unethical.
Diminishing Returns: After a certain point, increasing sample size offers little additional benefit.

Key Takeaways

Power analysis helps determine the right sample size, ensuring valid results.
Power of 0.80 (or higher) is commonly used to reduce Type II errors. Sample size impacts reliability, too small increases errors, too large wastes resources.
Balancing practicality and accuracy are essential when determining sample size.

Critical thinking Question

Why should researchers conduct a power analysis. Upon reviewing our lesson on alpha and beta levels, why else is it important to conduct?

Next Lesson: Confidence Intervals and Margin of Error (MOE)

Next, we will explore how confidence intervals help quantify the uncertainty in estimates and how to interpret the margin of error in research findings.